Question

Write an explicit formula for the sequence below...

Answer 1

Answer choices:

Answer 2

best way to do is, put n = 1 in each of you answer choices and see what you get. You know your 1st term should be 1/2.

Now if all of them gives 1/2 for their first term, Then try n= 2 and see which one gives you 3/7 for the second term.

Answer 3

@rajee_sam : Thank you! Could you go through the process with me though? I'm still a little confused.

Answer 4

my bad

Answer 5

15/199 is the answer to the second part of the question.

So lets do it all over again

the first answer choice for the sequence is

\[a _{n} = \frac{ (n + 1) }{ (n ^{2} + 3) }\]

Now for the first term put n=1

you will see \[a _{1} = \frac{ 1 + 1}{ 1 + 3 } = \frac{ 2 }{ 4 } = \frac{ 1 }{ 2 }\]

Answer 6

for the second term put n = 2

\[a _{2} = \frac{ 2 + 1 }{ 4 + 3 } = \frac{ 3 }{ 7 }\]

Answer 7

So this works and this is your rule for the sequence.

now for finding a14, put n = 14 in this sequence rule and find your answer.